Some results on almost eta-Ricci-Bourguignon solitons


Blaga A. M., Tastan H. M.

JOURNAL OF GEOMETRY AND PHYSICS, vol.168, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 168
  • Publication Date: 2021
  • Doi Number: 10.1016/j.geomphys.2021.104316
  • Journal Name: JOURNAL OF GEOMETRY AND PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
  • Keywords: Ricci-Bourguignon solitons, Gradient vector field, Torse-forming vector field
  • Istanbul University Affiliated: No

Abstract

We determine a formula to compute the defining function of a gradient almost Ricci-Bourguignon soliton by means of the potential vector field, providing in this sense two examples. We also give a rigidity result in this case. Moreover, we deduce some curvature properties of solitons with torse-forming potential vector field. Further we generalize some of the results to almost eta-Ricci-Bourguignon solitons and prove that a gradient almost Ricci-Bourguignon soliton on a doubly warped product manifold induces gradient almost eta-Ricci-Bourguignon solitons on its factor manifolds. (C) 2021 Elsevier B.V. All rights reserved.